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P does half work as compare to Q. R does half work as compare P and Q together. If R alone can finish it in 40 days, then all of them together will finish the work in how many days?

P does half work as compare to Q. R does half work as compare P and Q together. If R alone can finish it in 40 days, then all of them together will finish the work in how many days? Correct Answer 40/3

Let efficiency of Q be 2 unit/day

⇒ Efficiency of P = 2/2 = 1 unit unit/day

⇒ Efficiency of R = (2 + 1)/2 = 1.5 unit/day

Total work = 1.5 × 40 = 60 units

∴ P, Q and R together can complete the whole work in = 60/(2 + 1 + 1.5) = 60/4.5 = 40/3 days

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